Re: FindInstance question? Any ideas to solve this equality.
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- Subject: [mg128568] Re: FindInstance question? Any ideas to solve this equality.
- From: Dana DeLouis <dana01 at me.com>
- Date: Sun, 4 Nov 2012 20:12:12 -0500 (EST)
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- Delivered-to: l-mathgroup@wolfram.com
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Hi. I might hold off inserting machine numbers until later. Here's one idea:
data={
radiusV1->145.98630072715727,
radiusV2->95.62128455180272,
slopeV1Deg->9.462322208025617,
slopeV2Deg->18.43494882292201
};
Work with your equation. (I'll use t1 & t2)
(360*radiusV1)/(slopeV1Deg+360*timeV1x)==(360*radiusV2)/(slopeV2Deg+360*timeV2x)&&(360*(radiusV1*2))/(slopeV1Deg*2+360*(timeV1x*2))==(360*(radiusV2*2))/(slopeV2Deg*2+360*(timeV2x*2))
/. {timeV1x->t1,timeV2x->t2} ;
I find this easier to work with this:
equ = %//FullSimplify
radiusV1/(slopeV1Deg+360 t1)==radiusV2/(slopeV2Deg+360 t2)
Let's solve for t1:
FullSimplify[Solve[equ,t1]] [[1,1,-1]]
(-radiusV2 slopeV1Deg+radiusV1 (slopeV2Deg+360 t2))/(360 radiusV2)
Now, use your data:
%/.data // FullSimplify
0.051896 +1.52671 t2
So, t1 is equal to the above. If we subtract them, the equation is equal to zero.
t1-%
-0.051896+t1-1.52671 t2
f equals the above equation that is equal to zero.
f=%
-0.051896+t1-1.52671 t2
There really is no integer solution within a large range:
Minimize[{Abs[f],0<t1<10000000000,0<t2<10000000000},{t1,t2},Integers]
{0.578609,{t1->1,t2->1}}
As a side note:
If you Rationalized the machine numbers, you would have:
Rationalize[f,0]
-(3592760/69229991)+t1-(118038537 t2)/77315450
Try to use integers for t1 & t2
%*77315450 //FullSimplify
-(277775856142000/69229991)+77315450 t1-118038537 t2
Rearranged, you would have:
77315450 t1-118038537 t2 == 277775856142000 / 69229991
As you can see, there are no integer solutions for t1 & t2 that would give a rational number.
Even if you wanted to round the rational number, the solution is still not reasonable:
277775856142000 / 69229991 // Floor
4012363
Minimize[Abs[77315450 t1-118038537 t2-4012363],{t1,t2},Integers]
{0,{t1->471271145234969,t2->308683431630951}}
Minimize[Abs[77315450 t1-118038537 t2-4012364],{t1,t2},Integers]
{0,{t1->471271262689732,t2->308683508564028}}
Just throwing this out. You may find the function FrobeniusSolve and related functions interesting reading. However, it doesn't help here for this problem.
= = = = = = = = = =
HTH :>)
Dana DeLouis
Mac & Mathematica 8
= = = = = = = = = =
On Friday, November 2, 2012 11:54:28 PM UTC-4, Lea Rebanks wrote:
> FindInstance question:
> Hi All,
> I have evaluated the following equality with FindInstance function and
>
> there appears to be no results.
>
> Please could someone review the following equality to see if my result is
>
> TRUE or Is it possible to find one or more Integer results to this equality.
> Clear[radiusV1]
>
> radiusV1 = 145.98630072715727;
> Clear[radiusV2]
> radiusV2 = 95.62128455180272;
> Clear[slopeV1Deg]
> slopeV1Deg = 9.462322208025617;
> Clear[slopeV2Deg]
>
> slopeV2Deg = 18.43494882292201;
>
> Clear[timeV1x]
>
> Clear[timeV2x]
>
> FindInstance[(360*radiusV1)/(slopeV1Deg + 360*timeV1x) ==
>
(360*radiusV2)/(slopeV2Deg + 360*timeV2x) &&
>
> (360*(radiusV1*2))/(slopeV1Deg*2 + 360*(timeV1x*2)) ==
>
> (360*(radiusV2*2))/(slopeV2Deg*2 + 360*(timeV2x*2)) &&
>
> timeV1x > 0 && timeV2x > 0, {timeV1x, timeV2x},
>
> Integers, 2]
>
> {}
>
>
> Any help or advice gratefully received.
>
> Best regards,
>
> Lea=85